Details

analyze10.4s (27.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 39 to 24 computations (38.5% saved)

sample564.0ms (1.5%)

Algorithm

1×

intervals

Results

421.0ms	133×	body	1024	valid
61.0ms	35×	body	512	valid
35.0ms	71×	body	128	valid
19.0ms	17×	body	256	valid

Compiler

Compiled 82 to 52 computations (36.6% saved)

simplify76.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

103×	`unsub-neg_binary64`
90×	`associate-l_binary64`
88×	`distribute-rgt-in_binary64`
82×	`cancel-sign-sub-inv_binary64`
80×	`associate-r_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Status

Error

Program

▶

0.1b

(+.f64 lambda1 (atan2.f64 (*.f64 (*.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (*.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (*.f64 (sin.f64 phi1) (cos.f64 delta)) (*.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

Compiler

Compiled 114 to 69 computations (39.5% saved)

localize58.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite277.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
7.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2518 to 351 computations (86.1% saved)

series357.0ms (0.9%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

124.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
119.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
45.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
43.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))

Compiler

Compiled 3353 to 1830 computations (45.4% saved)

simplify264.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

460×	`distribute-rgt-neg-in_binary64`
439×	`cancel-sign-sub-inv_binary64`
438×	`neg-mul-1_binary64`
433×	`associate-l_binary64`
424×	`neg-sub0_binary64`

Counts

97 → 51

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	148	3100
1	318	2911
2	804	2872
3	1694	2872
4	3197	2872
5	4369	2872
6	5000	2872

prune179.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	44	7	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	7	52

Error

0.0b

Counts

52 → 7

Alt Table

Status	Error	Program
	28.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sqrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta))) (sqrt.f64 (.f64 (sin.f64 delta) (sin.f64 theta)))) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 2874 to 684 computations (76.2% saved)

localize83.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.3b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
0.3b	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
0.4b	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))

rewrite973.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

43×	`pow1_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
17×	`pow-prod-down_binary64`
16×	`sin-mult_binary64`

Counts

4 → 105

Calls

4 calls:

30.0ms	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
18.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))
15.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 10602 to 651 computations (93.9% saved)

series892.0ms (2.4%)

Error

0.0b

Counts

4 → 42

Calls

4 calls:

425.0ms	(/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
192.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
161.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))
50.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 6932 to 2709 computations (60.9% saved)

simplify543.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

316×	`distribute-rgt-in_binary64`
310×	`cancel-sign-sub-inv_binary64`
297×	`distribute-lft-in_binary64`
249×	`times-frac_binary64`
210×	`distribute-rgt-neg-in_binary64`

Counts

147 → 114

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	217	10049
1	554	9393
2	1912	8511
3	4751	8304
4	4977	8304

prune448.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Error

0.0b

Counts

121 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 4) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4)) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) 3) (pow.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))) 3)) (.f64 (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))) (+.f64 (pow.f64 (cos.f64 delta) 4) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4) (.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2))))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 7294 to 1329 computations (81.8% saved)

localize74.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)
0.5b	(pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)
0.5b	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3))

rewrite2.2s (5.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

190×	`cbrt-prod_binary64`
189×	`add-sqr-sqrt_binary64`
144×	`difference-of-squares_binary64`
133×	`unpow-prod-down_binary64`
123×	`times-frac_binary64`

Counts

4 → 301

Calls

4 calls:

36.0ms	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
19.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3))
15.0ms	(pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)
8.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)

Compiler

Compiled 19972 to 4042 computations (79.8% saved)

series944.0ms (2.5%)

Error

0.0b

Counts

4 → 44

Calls

4 calls:

379.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)
224.0ms	(/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))
198.0ms	(pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)
101.0ms	(cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3))

Compiler

Compiled 7460 to 3220 computations (56.8% saved)

simplify830.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

587×	`times-frac_binary64`
435×	`unswap-sqr_binary64`
249×	`exp-prod_binary64`
222×	`log-prod_binary64`
217×	`cube-prod_binary64`

Counts

345 → 319

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	423	36919
1	743	33920
2	2454	32701
3	4303	32701
4	5037	32701

prune331.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	318	1	319
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	319	8	327

Error

0.0b

Counts

327 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 4) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4)) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
▶	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 6) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 6)) 3) (pow.f64 (+.f64 (pow.f64 (cos.f64 delta) 4) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4) (.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2)))) 3))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
✓	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 8827 to 1758 computations (80.1% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)

rewrite278.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

4 → 62

Calls

4 calls:

4.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)
2.0ms	(pow.f64 (cos.f64 delta) 3)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))

Compiler

Compiled 5162 to 655 computations (87.3% saved)

series243.0ms (0.6%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

106.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)
69.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
28.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))
13.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 6311 to 2232 computations (64.6% saved)

simplify151.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

553×	`sqr-pow_binary64`
410×	`log-prod_binary64`
402×	`exp-prod_binary64`
333×	`*-commutative_binary64`
277×	`unswap-sqr_binary64`

Counts

94 → 43

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	2550
1	212	2274
2	677	2250
3	1652	2250
4	3222	2244
5	4704	2244
6	4994	2244
7	4906	2244

prune109.0ms (0.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	43	8	51

Error

0.0b

Counts

51 → 8

Alt Table

Status	Error	Program
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 4) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4)) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 3)) (+.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (/.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 6) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 6)) 3) (pow.f64 (+.f64 (pow.f64 (cos.f64 delta) 4) (+.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 4) (.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2) (pow.f64 (cos.f64 delta) 2)))) 3))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	17.7b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (sqrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))) (cbrt.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (cbrt.f64 (pow.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) 3)) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.1b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (/.f64 (-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (*.f64 (cos.f64 phi1) (cos.f64 theta)))))))))))
	0.2b	(+.f64 lambda1 (atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (.f64 (.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2)))) (/.f64 (cbrt.f64 (-.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))) 2))) (+.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (sin.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 theta))))))))))))

Compiler

Compiled 2344 to 487 computations (79.2% saved)

regimes3.2s (8.5%)

Accuracy

Total 0.1b remaining (46.1%)

Threshold costs 0.1b (46.1%)

Compiler

Compiled 127048 to 50470 computations (60.3% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`neg-sub0_binary64`
4×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	136
1	45	136
2	57	136
3	65	136
4	71	136
5	73	136
6	72	136

end1.0ms (0%)

Compiler: Compiled 86 to 29 computations (66.3% saved)

sample14.0s (37.3%)

Algorithm

1×

intervals

Results

9.8s	3940×	body	1024	valid
1.7s	1335×	body	512	valid
788.0ms	2174×	body	128	valid
733.0ms	535×	body	256	valid
100.0ms	16×	body	2048	valid

Compiler

Compiled 890 to 336 computations (62.2% saved)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Details

analyze10.4s (27.7%)

sample564.0ms (1.5%)

simplify76.0ms (0.2%)

prune6.0ms (0%)

localize58.0ms (0.2%)

rewrite277.0ms (0.7%)

series357.0ms (0.9%)

simplify264.0ms (0.7%)

prune179.0ms (0.5%)

localize83.0ms (0.2%)

rewrite973.0ms (2.6%)

series892.0ms (2.4%)

simplify543.0ms (1.4%)

prune448.0ms (1.2%)

localize74.0ms (0.2%)

rewrite2.2s (5.9%)

series944.0ms (2.5%)

simplify830.0ms (2.2%)

prune331.0ms (0.9%)

localize44.0ms (0.1%)

rewrite278.0ms (0.7%)

series243.0ms (0.6%)

simplify151.0ms (0.4%)

prune109.0ms (0.3%)

regimes3.2s (8.5%)

simplify8.0ms (0%)

end1.0ms (0%)

sample14.0s (37.3%)

Profiling

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55